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Answers to Chapter 10
Questions:
1. A derivative security is a financial security whose payoff is linked to another, previously issued security.
Derivative securities generally involve an agreement between two parties to exchange a standard quantity of an asset
2. A spot contract is an agreement between a buyer and a seller at time 0, when the seller of the asset agrees to
deliver it immediately and the buyer agrees to pay for that asset immediately. Thus, the unique feature of a spot
market is the immediate and simultaneous exchange of cash for securities, or what is often called delivery versus
payment. A forward contract is a contractual agreement between a buyer and a seller at time 0, to exchange a
prespecified asset for cash at some later date at a price set at time 0. Market participants take a position in forward
3. Trades from the public are placed with a floor broker. When an order is placed, a floor broker may trade with
another floor broker or with a professional trader. Professional traders are similar to designated market makers on
the stock exchanges in that they trade for their own account. Professional traders are also referred to as position
traders, day traders, or scalpers. Position traders take a position in the futures market based on their expectations
about the future direction of prices of the underlying assets. Day traders generally take a position within a day and
4. Clearinghouses are able to perform their function as guarantor of an exchange=s futures contracts by requiring all
member firms to deposit sufficient funds (called margins) to ensure the firm=s customers will meet the terms of any
futures contract entered into on the exchange. In turn, brokerage firms require their customers to post an initial
margin any time they request a trade. The amount of the margin varies according to the type of contract traded and
5. A long position is an order for a purchase of the futures or option contract. A short position is an order for a sale
of the futures contract.
7. a. If T-note futures prices fall a short position would be the profitable one to take.
b. If inflation in Japan increases by more than inflation in the U.S., the yen depreciates in value relative to the U.S.
8. An option is a contract that gives the holder (buyer) the right, but not the obligation, to buy or sell an underlying
9. A call option gives the purchaser (or buyer) the right to buy an underlying security (e.g., a stock) at a prespecified
price called the exercise or strike price (X). In return, the buyer of the call option must pay the writer (or seller) an
up-front fee known as a call premium (C). This premium is an immediate negative cash flow for the buyer of the call
A put option gives the option buyer the right to sell an underlying security (e.g., a stock) at a prespecified
price to the writer of the put option. In return, the buyer of the put option must pay the writer (or seller) the put
premium. If the underlying stock=s price is less than the exercise price (X) (the put option is Ain the money@), the
10. The call option on a T-bond futures contract allows the owner to buy the T-bond futures contract at a specified
price. For the owner of the option to make money, he should be able to immediately sell the bond at a higher price.
Thus, if the T-bond futures contract price increases, the writer of the call option makes a premium form the sale of
11. The put option on a stock allows the owner to sell the stock at a specific price. For the owner of the option to
make money, he should be able to buy the stock at a lower price immediately prior to exercising the option. Thus, if
12. First, if conditions are never profitable for an exercise (the option remains Aout of the money@), the option
holder can let the option mature unused. Second, if conditions are right for exercise (the option is Ain the money@),
the holder can take the opposite side of the transaction. Thus, an option buyer can sell options on the underlying
13. The Black-Scholes model examines five factors that affect the price of an option: 1) the spot price of the
underlying asset, 2) the exercise price on the option, 3) the option=s exercise date, 4) price volatility of the
The time value of an option is the value associated with the probability that the intrinsic value (i.e., the stock price)
could increase (if the underlying asset’s price moves favorably) between the option=s purchase and the option=s
expiration date itself. The time value of an option is a function of the price volatility of the underlying asset and the
time until the option matures (its expiration date). As price volatility increases, the chance that the stock will go way
up or way down increases. The owner of the call option benefits from price increases but has limited downside risk
The risk free rate of interest affects the value of an option in a less clear cut way. As the risk free rate increases, the
growth rate of the stock price increases. However, the present value of any future cash flows received by the option
holder decreases. For a call option, the first effect tends to increase the price of the option, while the second effect
14. The Securities and Exchange Commission (SEC) and the Commodities Futures Trading Commission (CFTC)
are often viewed as “functional” regulators. The SEC regulates all securities traded on national securities exchanges,
including several exchange-traded derivatives. The SEC’s regulation of derivatives includes price reporting
Since January 1, 2000, the main regulator of accounting standards (the Financial Accounting Standards Board, or
FASB) has required all FIs (and nonfinancial firms) to reflect the mark to market value of their derivative positions
The main bank regulators—the Federal Reserve, the FDIC, and the Comptroller of the Currency—also have issued
uniform guidelines for banks that trade in futures and forwards. These guidelines require a bank to (1) establish
internal guidelines regarding its hedging activity, (2) establish trading limits, and (3) disclose large contract positions
15. A swap is an agreement between two parties (called counterparties) to exchange assets or a series of cash flows
over a specific period of time and at specified intervals during that time period.
17. In an interest rate swap contract, the swap buyer agrees to make a number of fixed interest rate payments based
18. The bank could go Aoff the balance sheet@ and buy a swap; that is, take the fixed-payment side of a swap
agreement.
19. The firm would want to enter into a currency swap by which it sends annual payments in pounds to a swap
portfolio.
20. Caps, floors, and collars are derivative securities that restrict the interest rate variation on borrowed funds, i.e.,
they are options on interest rates. A cap guarantees that the rate on a loan will never go above a stated level. A floor
guarantees that the rate on a loan will never go below a stated level. A collar gaurantees that the rate will never go
Problems:
1. a. The settlement price is 99.3950 percent of the face value of the contract ($1 million).
2. a. You are obligated to take delivery of a $100,000 face value 15-year Treasury bond at a price of $95,000 at some
predetermined later date.
3. EXCEL Problem: Profit/loss = -$1,875
4. a. If interest rates increase over the period of investment, Treasury bond prices will decrease. Thus, Tree Row
b. Given a short position: Sale price of futures = 95-040 = 95 4/32% x $100,000 = $95,125
c. Given a short position: Sale price of futures = 95-040 = 95 4/32% x $100,000 = $95,125.00
5. a. If interest rates decrease over the period of investment, Treasury bond prices will increase. Thus, Dudley
Savings Bank should take a long position in the futures contracts on the Treasury bonds. As T-bond prices go up, so
will T-bond futures prices.
b. Given a long position: - Purchase price of futures = 105-100 = 105 10/32% x $100,000 = $105,312.50
c. Given a long position: - Purchase price of futures = 105-100 = 105 10/32% x $100,000 = $105,312.50
6. a. The investor has $40,000 ($1m. x 0.04) in his account. As a result of the decrease in value, the investor will
now be required to hold $38,000 ($950,000 x 0.04) in his account (or he has a $2,000 surplus). However, because
b. The investor is now required to hold $36,400 ($910,000 x 0.04) in his account. He has a $1,600 surplus ($38,000
- $36,400). But, because futures contracts are marked to market, the investor’s broker will make a margin call to the
c. The investor is now required to hold $39,000 ($975,000 x 0.04) in his account. He has a $2,600 deficit. Marking
d. The investor has $40,000 ($1m. x 0.04) in his account. As a result of the increase in value, the investor will now
be required to hold $42,000 ($1,050,000 x 0.04) in his account (or he has a $2,000 deficit). Because futures
7. a. The intrinsic value of the option is $4 (= $180 - $176). Thus, the time value of the option is $1 (= $5 - $4).
c. If the price of the underlying stock is $170 (less than the exercise price), you will not exercise the option. Thus,
the intrinsic value of the option is $0. In this case, the option premium is equal to the time value of the option is
$1.25.
c. The option holder will come to you to exercise the option. So, you must by the shares at their current market
9. a. If the price of the underlying stock is $29 (greater than the exercise price), you will not exercise the option.
10. a. If the price of the underlying stock is $32 (greater than the exercise price) and stays there until the option
b. The option holder will come to you to exercise the option. So, you must by the shares from the option holder at
b. The closing price of the December 12550 10-year Treasury bond futures call option was 1 47/64% $100,000, or
$1,734.375 on August 7, 2013.
d. The open interest on the September 2013 put options (with an exercise price of 153) on DJ Industrial Average
stock index was 1,379 on August 7, 2013.
12. a. Purchase option: -$2.17 x 100 shares
b. Purchase option: -$2.17 x 100 shares
c. With no exercise: purchase price = -$2.17 x 100 shares = loss of -$217 versus a loss over -$167 if you exercise
13. a. Purchase option: -$1.25 x 100 shares
b. The option never moves into the money, so it would never be exercised.
14. You will make a profit on the option if the MMC stock price rises above 17.83, i.e., $15 + 2.83.
16. a. Premium for purchasing the cap = 0.0065 x $200 million = $1,300,000. If interest rates rise to 10 percent,
b. If the FI also purchases the floor: Premium = 0.0069 x $200 million = $1,380,000, and the total premium =
If interest rates rise to 11 percent, the cap purchaser receives 0.02 x $200m = $4,000,000, and the net savings =
If interest rates fall to 3 percent, the floor purchaser receives 0.01 x $200 million = $2,000,000, and the net savings =
c. If the FI sells the floor, it receives net $1,380,000 minus the cost of the cap of $1,300,000 = +$80,000.
17. a. The insurance company (IC) is exposed to falling interest rates on the asset side of the balance sheet.
c. The IC wishes to convert the fixed rate liabilities into variable rate liabilities by swapping the fixed rate payments
d. The FC will make fixed rate payments and therefore is the buyer in the swap. The IC will make variable rate
e. A possible diagram is as follows:
Insurance Company Swap Cash Flows Finance Company
Note that the fixed rate swap payments from the FC to the IC will offset the payments on the fixed rate liabilities
now have cash flows from interest income and interest expense that much closer match.
18. a. The commercial bank is exposed to a decrease in rates that would lower interest income, while the savings
Savings Bank Swap Cash Flows Commercial Bank
c. As a result of the swap, the commercial bank has transformed its fixed rate liability CDs into a variable-rate
liability matching the variability of returns on its loans. Further, through the interest rate swap, the commercial bank
19. a. Money Center Bank Savings Bank
Cash outflows from
balance sheet financing -8% x $400m -(CD rate) x $400m
As a result of the swap, the money center bank has transformed its four-year, fixed-rate liability notes into a
variable-rate liability matching the variability of returns on its C&I loans. Further, through the interest rate swap, the
b.
End of One-Year One-Year Cash Payment Cash Payment by Net Payment
Year CD rate CD rate + 1% by MCB Savings Bank Made by MCB
1 8% 9% x $400m $ 36m (8%x$400m) $ 32m $ 4m
The savings bank’s net gains from the swap in year 1 are $4 million per year. The enhanced cash flow offsets the
increased cost of refinancing its CDs in a higher interest rate environment; that is, the savings bank is hedged against
c. The money center bank receives income of CD rate + 4% on its assets and pays CD rate + 1% on its existing debt
and the swap. The savings bank receives 9.5% on its assets and pays 7% on its existing debt and the swap.
Year NI MCB NI Thrift
Both FIs have completely insulated their net income against changes in interest rates. The money center bank’s net
income is $12 million each year. The savings bank’s net income is $10 million each year.
20. a. Bank Savings Association
Cash outflows from
Rate available on:
Variable-rate debt T-bill + 2½%
As a result of the swap, the money center bank has transformed its four-year, fixed-rate liability notes into a
variable-rate liability matching the variability of returns on its C&I loans. Further, through the interest rate swap, the
b.
End of One-Year One-Year Cash Payment Cash Payment by Net Payment
Year T-bill rate T-bill + 2¼% by Bank Savings Association Made by Bank
1 4% 6¼% x $200m $12.5m (10%x$200m) $20m -$7.5m
2 3 5¼ 10.5m 20m -9.5m
Overall, the bank made a net dollar gain on the swap of $31.5 million in nominal dollars and the savings association
made a net payment of $31.5 million.
Year NI Bank NI Savings Association .
1 (8% - 5¼%) × $200m = $5.5m (13% - 10.75%) × $200m = $4.5m
